Enzyme Perfection

Since teaching biochemistry for the first time last semester, I’ve widened my reading to include general aspects of biochemistry that may help me see the big picture and educate myself! I just finished a short book by Athel Cornish-Bowden titled The Pursuit of Perfection. The author chooses interesting vignettes in biochemical evolution to probe the question of whether extant biochemistry is optimal in some sense. How and why did enzymes evolve to what they are today? Today’s blog post is on the first chapter, “Some Basic Biochemistry”.

 

Likely, the first thing that students learn about biochemistry even before they step into a formal biochemistry class, is about enzymes. Enzymes are crucial biochemical catalysts. Without them, biochemical reactions that involve making and breaking covalent bonds would be much, much slower! But why do we need enzymes? There are many other ways of increase the rate of a chemical reaction. You can heat it up, you can apply pressure, you can provide mechanical or electrical energy, and it works. But the problem with these approaches is that they often lack specificity.

 

The author puts it this way: “Why should we be impressed at the capacity of enzymes to do the same thing? The fact that an enzyme can do it at low temperatures is part of the answer, but the really impressive aspect of an enzyme is no that it is a good catalyst for a given reaction but that it is an extremely bad catalyst – no catalyst at all, in fact – for virtually every other reaction.” If you were at much higher temperatures, all sorts of unwanted reactions are also taking place, and achieving fine-tuned control is very difficult. That’s why biochemistry tends to only occur under a narrow range of “mild” conditions. Yes, there are some organisms that live in “extreme” environments, but from a universal perspective these conditions are still very narrow.

 

There is a conundrum, however. If enzymes are specific, they also have to be much larger in size than the reaction they are catalyzing. But why? First the author disposes of a misunderstanding stemming from our perception of “things we can handle”. We think linearly. His example: “If we say that a bed is a bit bigger than a person, we mean… that it is a bit longer than the person who sleeps in it. The fact that it is a lot higher and a lot wider, so that its volume is much larger than that of the person who sleeps in it…” He estimates that “an enzyme is typically 50-100 times larger than the combined volume of the molecules it acts on…” For comparison, “a volume ratio of 70” is typical for a car with a single passenger. For an office with a volume ratio of 70, it would feel tight – like a small closet or cubicle. A rough estimate of my office volume was 300 times my own volume, which was higher than the author’s average of a 200-fold volume ratio for a relatively comfortable office. I feel lucky!

 

Now to the issue at hand. A smaller enzyme would require fewer resources to biosynthesize. It’s energetically costly to make bigger enzymes with more atoms! Why does it need to be so big? The author writes: “An enzyme is a precision instrument, capable of recognizing its substrates, distinguishing them from other molecules of similar size and chemical behavior, and transforming them in precise ways. In general, the more precise any instrument has to be the bigger it must be, and the relative size difference between an enzyme and the substance that it acts on, is not very different from what you would find if you compare a precision drill with the object to be drilled, if you include the clamps and other superstructure as part of the drill.” I had honestly not thought about it that way before, but it makes good sense, and I’m filing this mental picture for future reference!

 

But there’s more. An additional constraint is that the enzyme must be “extremely unreactive when not in the presence of the molecules they are intended to transform, to make sure that they do not undergo any unwanted reactions… This is much for difficult for working on a very small molecule than it is for a large one, and we sometimes find that the largest enzymes work on the smallest molecules, and vice versa.” Eeeks! I didn’t know this when I was teaching biochemistry and I wish I did. It makes sense to me, but I just never thought about it that way. Another factoid to be filed for future reference! The author uses the examples of pepsin and catalase to bring his point home.

 

And then I learned that the reason why we need catalase, and quite a bit of it, in our blood. It converts hydrogen peroxide (H₂O₂) back into water and oxygen gas. The author lucidly explains: “… any living organism needs to be able to destroy harmful chemicals… that get into cells. There are a great many potential hazards of this kind, and as the cell cannot prepare a separate solution to every conceivable problem that might arise, it deals with many unwanted chemicals by making them react with oxygen… This is a useful step, for example, toward making insoluble poisons soluble in water, so that they can be excreted…” Hence general-purpose (i.e. less specific) enzymes have evolved for this sort of business but they also oxidize water in the process turning it into H₂O₂, which can be toxic at higher concentrations, so catalase needs to get rid of it. (At lower concentrations H₂O₂ acts as a signaling molecule, which is what you might expect evolutionarily – poisons get co-opted into signalers.)

 

All this took the author just a few pages and I learned so much! I felt very humbled and reminded that I have a-ways to go before I start to think like a biochemist, but hopefully I’m on the right road. With help from others!

A Spherical Cow

Many years ago, I learned from physics colleagues that when asked to solve a ‘real-world’ problem, they begin with the statement: “Consider a spherical cow…” Little did I know that this is also the name of a book, and my university library had a copy (of the first edition published in 1985). Consider a Spherical Cow is written by John Harte, a professor at UC-Berkeley. It is subtitled “A Course in Environmental Problem Solving”.

 

The book presents 45 problems with worked solutions with interesting ‘real-world’ applications related to geoscience. Each of the ‘solutions’ discusses the approximations made when a simpler model is used (akin to the spherical cow) but also includes discussion and follow-up exercises (no solutions provided) if the model was modified to take more complicated features. Essentially, a cow isn’t really a sphere, so how do we account for that?

 

Chemistry features prominently in a number of the problems. There are problems of atmospheric chemistry, natural elemental cycles (carbon, nitrogen, sulfur, phosphorus). Some problems feature acid rain, trace metal mobilization, fossil fuel burning, and more; for example, “What is the pH in pristine precipitation?” No, it’s not seven. There are several thermodynamics and energy transfer type problems. There are also a number of ecology-type problems including an interesting one about how the population of China might change and when it might approach steady-state. It begins with 1980 data and predicts trends going forward in different age bands every decade through 2040. Today we can compare how well those initial models worked. The results are interesting, and Harte does a good job in discussing the caveats in any model.

 

The math is mostly algebra, albeit quite involved. There is a little bit of vector notation and the occasional differential equation, but these can essentially be transformed into algebraic problems. The appendix has data which students can draw from to solve these ‘real-world’ questions. Since I’d been thinking of transforming my G-Chem courses to include a chunk of data-science techniques, I found Harte’s approach helpful to think about even if I will likely not use many of the actual problems that he poses. It’s the habit of mind that we’re trying to inculcate in our students: how to approach a problem by constructing a simple (model) first and then iteratively improve upon that first guess.

 

I recommend Harte’s book if you are interested in seeing the workflow in his book starting with warm-up exercises and progressing to beyond back-of-the-envelope approaches. I’d also like to come up with the chemists’ equivalent of “Consider a Spherical Cow”. Any suggestions?

Lonely Hobbit, Victory Rout

This year I’m having another resurgence in playing Origins: How We Became Human. I had gotten into it back in 2021 and wrote a couple of blog posts. If you’re unfamiliar with the game, I suggest reading this overview. For today’s session report, I took fewer notes. I was playing Hobbit and I thought I would do poorly given an unfavorable climate change causing me to be isolated with little room to expand or build. But I managed to turn things around and romp to victory. You can also read a more flavorful session report with a global view (where I came in second place as Hobbit). But on to the action!

 

Back maybe a hundred thousand years ago…

 

Turn 1: A diminutive tribe imitates group mating rituals from their taller northern neighbors. In addition, they learn to scrape hides and a new profession emerges: the leatherworker! Something opens up in the limbic system of their brains – technical knowledge!

 

Turn 2: Some astronomical event triggers climate change, and impassable and dangerous jungles expand all around. The ‘hobbits’ are hemmed in with nowhere to go. But their brains expand to acquire natural knowledge and the rudiments of language. Basket-weaving becomes a major activity.

 

Turn 3: A Milankovitch cycle triggers a tropical age with a rise in ocean levels. There is little land and the new species are hemmed in on a tiny tropical island. [Pictured: The green cube on the Hobbit starting spot is isolated because of the two climate changes. Can’t move. Can’t expand.]

 

Turn 4: Inexplicably, sudden global cooling occurs and an ice age returns! [This is very rare! It requires a six to be rolled the turn before due to a climate card being drawn, and another in this turn. There aren’t that many of these cards.] The hobbits quickly expand into Sulawesi and are able to domesticate the water buffalo, but they catch a zoonotic disease and develop child swaddling.

 

Turn 5: Land south beckons as the hobbits discover land in a large continent to the south. [Pictured below: Australia!]

 

Turn 6: Kayaks are developed and fishing becomes a huge industry. The hafted thrusting spear is invented and hobbits enter the Copper Age. Using a hammer and anvil to crack nuts brings more nutritional access.

 

Turn 7: The diprotodon wombat in the Australian desert is domesticated into a warbeast! Hobbits enter the Bronze Age [ahead of the other players].

 

Turn 8: [Neanderthals cultivate wheat and advance to Era II and the Bicameral Age first.] Hobbit women begin to practice sham menstruation to reduce the number of children. With kayaks and bronze tools, adventurous groups hack their way through the jungles to the north into China.

 

Turn 9: Millet is cultivated but at low protein value. However, Hobbit society is doing well and productive overall. [My innovation level is at 4 even while I’m still in Era I; I had never achieved this before.]

 

Turn 10: [Cro-Magnons advance to Era II, Peking Man who has been doing poorly enslaves themselves to the advanced Neanderthals so they can quickly increase their footprint.] Hobbits fail to cultivate soybeans (twice)!

 

Turn 11: [Cro-Magnons and Neanderthals advance to Era III, Peking Man freed and quickly acquires a metropolis.] Hobbits finally cultivate soybeans but it is also low protein. They begin to practice burials and expand their language finally moving into Era II. It’s the bicameral age and we are starting to develop more self-awareness.

 

Turn 12: Culturally, body paint and shell necklaces become a new status symbol. The climate becomes mild becoming more of a Parkland – the jungles disappear. We start to build ziggurats and can boast of a rich culture.

 

Turn 13: A group of adventurers makes it to the Maldives but then are infected by diphtheria from the Africans in the continent west of us. We learn new food storage techniques. We are able to cultivate coconuts [thereby getting to the important Footprint level 3]. Temple administrators become the governors in our society. We move into Era III, the Age of Faith.

 

Turn 14: We develop the iron ploughshare and become the first to reach the Iron Age. This superior metallurgy puts all other nations on notice. We develop public baths and the new professional class of architects is held in high esteem!

 

Turn 15: The outrigger canoe is invented and our adventurers discover a new world across the Bering Straits.

 

Turn 16: The Africans hit with a barbarian raid on the Maldives. A serious drying and desertification takes place all over the globe. Our spies practice espionage on our enemies. Islam becomes our dominant religion.

 

Turn 17: The volcano Kikai erupts. It is felt by our metropoli in the northeast but there is no severe damage or loss of life. Our spies help us to develop hieroglyphs. Our engineers build trireme galleys. We take mathematics seriously and build Aristotelian schools. A new settlement is founded in Hawaii.

 

[I stopped to take photos at this point. I’m Player Green with metropoli in Asia, Hawaii and the Maldives. Neanderthal is Player White and occupies western Europe and Africa. Peking Man is Player Red in Central Asia. Cro-Magnon is Player Black in East Africa.]

 

[I’m the only player in the New World. You can also see in the Development tree that I’m on par with Neanderthal in all areas. In some areas, Cro-Magnon and Peking Man are slightly behind.]

 

[Here’s my player board. My innovation is at 3 which is pretty good and I have three producers and one consumer. I need to increase this.]

 

Turn 18: Biofuel extraction in Hawaii is successful! [I’m the first to advance to Energy level 2, a sign that I’m now in the lead, which means the other players might start collaborating.] We quickly expand into Venezuela and establish a metropolis to prospect for oil.

 

Turn 19: Thera erupts in the Mediterranean. We develop terraced agriculture [moving to Footprint level 4]. Our society enters a golden age of feudalism. [We must be in the Middle Ages now?]

 

Turn 20: Yellowstone erupts. [That’s a lot of volcanoes in the last several turns! Not so common.] There is also significant climate change causing deserts to retreat and reestablishing a milder savanna climate. We domesticate the Camelops in North America and develop a battering ram tank for war. Attempts to extract for oil fail. [I need to roll a six on each attempt.]

 

Turn 21: Our society is struck by bubonic plague, we start to develop drugs and medicines. We’re the first to advance into Era IV, the Age of Reason. It’s a renaissance!

 

Turn 22: Many social changes come about: humor becomes popular, courtesans become active, marriage dowries are practiced, and monogamy becomes dominant. We strike oil in Venezuela! [This brings me to Energy level 3 and Metallurgy level 4, the Gunpowder Age. I can now easily siege and take over metropoli from other players.]

 

Turn 23: [Neanderthal makes it to Era IV] A court system is developed and lawyers abound throughout our society. We turn to world conquest, besieging other cities, and foreign workers fill our pool of laborers and artisans.

 

Turn 24: Our society undergoes a revolution from a social equity society to one that favors individual freedom. We enter a golden age of entrepreneurship.

 

Turn 25: [I reach Energy level 4] So many things are invented: steam engines, pharmaceuticals, aluminium smelting and plastics. [I also advance my Maritime and Metallurgy levels.] Broadcasting takes root and ‘couch potato’ becomes a new phrase in our vocabulary. We also invent the personal computer and software programmers are highly sought after. Videogames become popular. [These last few cards are ‘Utopia’ cards that help me trigger the Game End by modifying a die roll. I am successful and the game ends.]

 

[I rule most of the world and have hemmed in my opponents.]

 

[In advancements, I’m clearly ahead in Energy, Maritime and Metallurgy.]

 

[I have lots of producers with lots of foreign workers, the non-green cubes. My innovation and population are at their maximum.]

 

I win the game with a final score of 48 points. This is very high in my experience of 4-player games. The other players are far behind (Cro-Magnon 14, Peking Man 8, Neanderthal 13) so my victory was a rout. Some games are like that, others are much closer.

 

P.S. If you liked reading these session reports, here’s one on boardgamegeek.com where I came in second as Neanderthal.

The Expanse

A while back, I read the first three books of The Expanse series, which I enjoyed and is a good temporary stopping point. Several months ago, I discovered that my local library was ordering the DVD box set of the full six-season TV series. I’d heard good things about it. I decided to first read Books 4-6 before starting on the TV series. Then my spouse and I slowly watched our way through the visual version of The Expanse.

 

Overall, I would give two thumbs up to the TV series. They did a good job adapting the books to the visual medium. This is always a challenge. I felt there was a bit of a rough start to Season 1. My wife, who had not read the books, was confused in the first several episodes. Even though I knew the story, I still found the presentation confusing. I understand the strategy of plopping the viewer dab smack in the middle of the action without much explanation (some scifi revels in this), but in this case I thought it was less than effective. Thankfully, things started to cohere as the season progressed and I feel that a certain consistency emerged over time.

 

[SPOILERS from here on…]

 

The TV series blends in background information and characters from future books by introducing them earlier in the season. Avasarala who only shows up in Book 2 begins to be featured in Season 1, and I think they did this effectively. Havelock also showed up in Season 1, but was inexplicably absent in Season 4. I can see why they cut out chunks of that story to concentrate on what was happening in Ilus. You have to make choices of what to keep and what to cut. Overall, the TV series has fewer characters from the book, as expected. Some are composite characters. For me, the most interesting choice was to introduce Drummer early and progressively make her a single main character by taking on the roles of other key characters. This was very well done, and the show-writers did an excellent job in using their freedom to create a compelling character.

 

An engaging scifi book is often more about probing the social science aspects rather than getting into details of the ‘hard’ science. This, I think, is a very effective approach. You need to provide enough to make the world feel realistic, but be vague enough so that your reader doesn’t suffer from disillusionment because you introduced something more ridiculous than fantastic. You can be vague in a book and leave imagination up to the reader but this is not so easy in the visual medium where you now have to decide how you will represent the technology. The Expanse TV series is a mixed bag. Some of the visuals are absolutely spot-on and I felt immersed in their world. Others were more meh and broke the spell of illusion. But overall, I like their representations of the Belt space stations, and the PDC countermeasures against torpedoes made for exciting visuals. Seeing the Nauvoo first get towed out was awesome.

 

I didn’t recognize any of the actors in the series. That was a good thing. Most of them did not look like what I might have imagined when reading the books, so while I experienced some cognitive dissonance in the early goings, eventually I felt that the main-billed actors inhabited their characters and I think they made excellent choices overall. No one was a dud. Drummer was superbly portrayed and one of the most engaging presences on-screen, which I find interesting given that she was a composite of multiple characters in the books. I suspect that going forward when I read Book 7, I will start to picture the TV series actors instead of what I had imagined previously in my mind’s eye. Not sure if this is a good or bad thing.

 

Finally, as a chemist who studies the origin of life, the protomolecule is of particular interest to me. I was less impressed by the visuals involving the protomolecule. And now that I think about it, the name is highly misleading. There’s no way a single molecule (even one that is large and multifunctional) can do what it purports to do – feed on organic matter and activate it into something life-like that straddles the boundary between machine and organism. It has to be a protomolecule system. But adding the word system would sound clumsy. Mixture? Composite? I can’t think of a better word, but the use of the singular-sounding protomolecule entrenches a wrong conception of how chemistry works. And the protomolecule’s action is all about chemistry.

 

Maybe after finishing Books 7-9, I will revisit what I think the protomolecular system needs to consist of. I study protometabolism. Maybe that’s what they should have called it: the protometabolism – but that would likely have been confusing. But that’s for another time. Watching the series also made me think of the “curse of knowledge” that inflicts all teachers. We have to constantly try our best to put ourselves in the shoes of our students to anticipate what will be confusing to them. If you haven’t read the books, parts of The Expanse TV series will be a bit of a muddle. My spouse would still say she found it engaging, and she was able to follow most of it with no problems. I did clarify some of the parts she found muddled, but overall that was minimal except for the early going in the first season. I am happy to recommend The Expanse TV series if you’re looking for engaging characters and an interesting multifaceted story.

Ends and Odds

If you wait long enough, everything goes to equilibrium – a strange state of balance where it looks like nothing is changing. But look more closely and you see a frenzy of activity that seems to go… well, nowhere. Why?

 

A macroscopic process seems irreversible. A drop of ink in water spreads out and smears until it uniformly colors the liquid. You’ll never see the colored liquid turn back into colorless water and an ink droplet. But at the microscopic level (actually nanoscopic), the motion of jittery molecules does not distinguish between forward and reverse. Molecules just keep moving back and forth, and forth and back. Our experience is that macroscopic processes are unidirectional along the flow of time, while microscopic processes are time-reversible – you can’t tell if it’s going forwards or backwards and it makes no difference.

 

I’ve been reading Knowing by Michael Munowitz and enjoying his lucid explanations into the nature of… well, nature. Today’s post is about Chapter 10, aptly and cleverly titled “Ends and Odds”. It’s about thermodynamics. It’s about the fate of all macroscopic processes (to reach equilibrium!). It’s about the elusive nature of time, flowing unidirectionally toward greater and greater entropy. It’s about statistics. What makes the time-agnostic microscopic world into the one-way flow of the macroscopic world is a matter of odds. Munowitz declares this is about freedom. While the frenzy of the jittery microscopic motion never stops, this “freedom [of motion] leads to equality: freedom of position, equality of distribution.” This is what it means to be at equilibrium.

 

Munowitz walks the reader through three examples: pressure, temperature, and distribution. Molecules freely move until all pressures equalize, all temperatures equalize, and all concentrations equalize. It all comes from statistics. Considering pressure, Munowitz writes that it “arises from the impacts of individual molecules against the walls of a container. Each single impact is small, yet there is strength in numbers. The collisions come rapidly and in tremendous quantity, averaging together to produce a steady macroscopic pressure at equilibrium: a statistical average, emerging clear and sharp from the microscopic confusion. Microscopic randomness gives way to macroscopic reliability.” The same thing happens for temperature and distribution (concentration). Macroscopically there is a reliable one-way gradient. Heat flows from hot to cold. Solute molecules flow from a more concentrated area to a less concentrated one.

 

Here are a few more quotes from Munowitz that I liked:

·      “Always in motion, microscopic particles exchange energy and influence as they slip into a state of equilibrium… We need to understand particles as crowds, and we need to understand them as individuals and small groups. For the many, we need statistics.”

·      “To be in equilibrium is to lose track of time, to disappear the into the gray sameness of an unchanging macroscopic state… Without change, time disappears. The clock ceases to tick.”

·      “Once a system attains equilibrium, all memory of the past is gone. Looking at the present, nobody can say when the system got, how it got there, why it got there… The scant macroscopic information to be gleaned (… constant this, constant that) provides no clue to what came before. It Is, at least for the present, the end of history.”

 

An equilibrium can be stable; it can be unstable; or it can be metastable, as shown by these three pictures from left to right.

 

Munowitz writes: “a stable equilibrium need not last forever, because stability is always a matter of where one sits in relation to some other possible state… Hit any equilibrated system hard enough, and it will awaken as if from a slumber… there can be a second at after equilibrium, and more than that, too: there must be activity during equilibrium. How else could a quiescent system, lost in the macroscopic timelessness of equilibrium, be able to accept a better offer and embark on a new history? To do so, it must tap a power that comes from within. It must draw upon a microscopic power belied by an overall macroscopic calm.” Munowitz will explain this with the help of two friends, Mack and Mike, and their glaringly different perspectives. I encourage you to read Knowing for the full glory of his prose, here are just snippets:

 

“To Mack, our macroscopic observer, equilibrium is a static affair: a tableau, timeless and unchanging, a still photograph rather than a movie. Except for the occasional fluctuation, which flickers briefly and then disappears, there is nothing to report…”

 

“To Mike, a microscopic observer, equilibrium offers a restless, dynamic picture of infinite variety. Atoms and molecules move this way and that… Some speed up, and some slow down. They smash together an come away with new structures… Microscopic equilibrium is a movie with a cast of zillions, and every frame is different…”

 

“But even as Mike’s fine-grained movie plays on, with one inexhaustibly rich image giving way to another, Mack still sees the same scene frozen in time… with one macroscopic state... Run the tape backward, forward, in random sequence, in whatever way you like – it makes no difference… Meanwhile the microscopic actors work furiously only to have the system stay in place. Atoms and molecules, colliding unceasingly, exchange energy… they vibrate…  interact with fields… reconfigure their electrons… break into bits… react chemically… The give and take of energy never stops, but at equilibrium only the one microstate endures. The microstates partition the total energy in different ways, yet still the equilibrium microstate remains the same.”

 

Mack is amazed by the rich world of interactions that Mike describes. Mack wants to know what is “the special force that guides a system unerringly (almost eerily) to equilibrium and subsequently defends the stable state so stubbornly against small fluctuations.” It’s a mystery to Mack and wants Mike to explain. Mike is confused and says “What mystery? What special force? I see nothing but a lot of little molecules obeying the ordinary laws of mechanics exactly as they should. Believe me, there is nothing unusual going on here.”

 

Maybe not unusual, but something is going on. Munowitz calls it “the law of the land in the Land of the Big, the Many, and the Simple.” It’s statistics. The odds are what leads to the end. But if there’s an end, there’s a beginning. Time moves in one direction, at least that’s our experience as macroscopic organisms. The freedom that leads to equality of distribution drives this process inexorably forward. Entropy reigns supreme over large time scales. Munowitz writes: “Later means a world in which a fixed quantity of global energy has spread to a large number of recipients. Later means a world in which useful energy… has become just a little bit harder to find, a world that has yielded just a little bit more to the relentless pull of statistics.”

 

Today in my statistical thermodynamics class, I waxed poetic about fate and destiny. I derived the equations showing how and why chemists introduce the Gibbs Free Energy. I drew pictures. I grimly talked about the entropy tax that must be paid for any chemical reaction being leveraged to do useful work. I’m not sure if the students shared my rhapsodizing enthusiasm. I’m thinking of assigning them Chapter 10 since Munowitz says it all much better than I do. It’s all about Ends and Odds.

Classifying Failures

To err is human. Sometimes it’s necessary. Sometimes inevitable. But is it ever desirable?

 

Perhaps, there’s a Right Kind of Wrong, the title of Amy Edmonson’s latest book. Edmonson is a professor of leadership and management with a diversity of work experience before she entered academia. The subtitle of her book: “The Science of Failing Well.” The gist of her book is arguing that it is useful to classify three types of failures (intelligent, basic, complex) and be cognizant to your situation – you need to practice self-awareness, situation awareness and system awareness. A key ingredient to failing well is to have high standards but also be in an environment of high psychological safety – you’re not afraid to own up to the failure because you will be supported by those around you. Let’s take these in turn. 

 

An intelligent failure is when you learn from failure in a novel situation. When you encounter something you’ve never done before or new to you, the only way to make progress is trial and error. Getting things wrong is inevitable. Edmonson brings up the example of a research lab. You’re pushing into the unknown and you will try a lot of things that fail before you succeed. It’s something I try to impress upon my research students; I typically gesture to my file cabinet of abandoned projects. If you don’t try, you won’t succeed. But you’ve also got to know when to throw in the towel, and that’s a skill that takes time and experience (and hopefully good advice from mentors). So it’s important to ask yourself: Am I in a novel situation?

 

A basic failure takes place in well-trod territory. It’s truly an oops! You should have known better, especially since you’ve done this before. But sometimes overconfidence and not paying attention can lead to an error. The consequences could be small; the consequences could be devastating. Regardless, you must try to learn from it so you can avoid repeating it in the future. On the other hand, a complex failure is not so easy do diagnose. I’ve previously blogged about this after reading Charles Perrow’s classic Normal Accidents. Such errors occur when there are complex interactions among multiple parts in a tightly-coupled system. System failure always has multiple causes. Again, paying attention is crucial, especially to early warning signs.

 

A first ingredient to learn from failure is being self-aware. Even so, failure feels like a letdown and your first instinct is to beat yourself up over it, or worse to ignore it and shift the blame. Edmonson’s advice: “Choose learning over knowing” and reframe a failure as an opportunity to learn. That requires taking a pause and not acting on that pernicious first instinct. To be situationally aware, ask yourself what context you are in. Is it novel? Is it routine? Is something different than before? Is this part of a complex system? You also have to rate the consequences: Is this a low-stakes or a high-stakes situation? If low-stakes, taking a risk so you can learn might be desirable; if high-stakes you might want to think twice before betting the farm. The stakes may be physical, financial, or reputational.

 

It’s hard to be system aware. Ever since I dipped into systems chemistry, I’ve often found myself lost in a tangle. Thinking systemically can also be discouraging; sometimes you feel stuck in a system and there seems to be no easy way out. Edmonson outlines a simple scenario she often uses called the Beer Game, a seemingly simple scenario where students play four roles in a supply chain: “factory, distributor, wholesaler, retailer”. The rules are simple. The retailer picks a card providing the demand for that turn and then each player makes orders and keeps track of inventory. But there’s a lag time as inventory makes its way through the system. Things go awry in a hurry. There’s a tiny and surprising catch in the game that surprises students, but I won’t give it away; read Edmonson’s book or look it up. Edmonson admonishes the reader to “anticipate downstream consequences”, “resist the quick fix”, and “redraw the boundaries”. Per the typical business book, she provides lively anecdotes, engaging examples, and a positive self-help vibe.

 

Reading this book made me ask myself if I am risk-averse. Do I try to avoid failing? Partially, I suppose. Research is probably an area where I’m not risk-averse. But I don’t dump all my eggs into one basket and usually juggle multiple investigations to increase the chances of success. But I’m protective of my time, and that makes it difficult for me to make a large pivot. I sometimes imagine being able to do so, but then step back and do incremental small changes. This is also true of my teaching. I’m always trying new things, but in small increments. Edmonson made me pause and think about where I can shake things up for a much better payoff especially since almost everything I do as a professor is low-stakes for me.

 

How about my students? These days students seem much more risk-averse than when I started teaching. Getting a B or a C on an exam can seem like a devastating outcome. I’ve designed my class with lots of low-stakes ways students can engage in the “struggle” to learn the material. Chemistry is novel, and it’s certainly not easy. I’m upfront with my students about this, but I hopefully also convey that they can all learn it if they’re willing to put in the time and effort. But I recognize that if students don’t feel psychologically safe, then they won’t be willing to take the risk and make mistakes as part of learning. As a result, they don’t learn as well as they could. Right Kind of Wrong has challenged me to think about how I can help the students gain better situational awareness and see learning as a transition from novel to variable to routine such that when you’ve practiced a lot, you really do have the material down pat.

 

I tell students to make their mistakes in class and on the low-stakes homework and quizzes so that they won’t make them on exams. Making mistakes when learning new subject matter is inevitable, even necessary. To err is to (hopefully) learn.

Theory of Learning and Evolution

I recently read three papers by Vanchurin (and colleagues) that builds a theory of learning and illustrates its generality in reference to machine learning, biological evolution, and the (presumably physico-chemical) origin of life. Math is involved, and I found some parts can be difficult to follow. But the writing is clear and the progression of the argument methodical. Today’s blog will only focus on one of these, the most conceptual of the three: “Toward a theory of evolution as multi-level learning.” (PNAS 2022, DOI: 10.1073/pnas.2120037119). I will be quoting the paper often my paraphrases will be clumsier than their clear prose.

 

What drives evolution in biology? Essentially, “solving optimization problems, which entails conflicts or trade-offs between optimization criteria at different levels or scales, leading to frustrated states…” There are three important pieces here: (1) optimization, (2) an interplay of distinct timescales in a hierarchical system, and (3) non-ergodicity that arises from competing interactions (the “frustrated states”).

 

The paper begins with seven basic principles. The first, and most important, is the existence of a “loss function of time-dependent variables that is minimized during evolution”. To stay alive is to solve an optimization problem. There needs to be some sort of learning that comes from an organism interacting with its environment. And when you’re dealing with the open unknown, the best solutions we know of involve “implementation of a stochastic learning algorithm”. Thus, learning and evolution are “optimization by trial and error”.

 

The next three principles, still very general, cover the following:

·      There’s a “hierarchy of scales”, each of which has its own “dynamical variables that change on different temporal scales”.

·      These timescales are distinct.

·      The faster-changing variables can be statistically defined by the slower-changing ones. (In thermodynamics, we can use macroscopic parameters to encompass the cacophony of the microscopic world.) This is known as Renormalization.

 

The final three principles are more specific to the living systems of Planet Earth, a sample size of one. “Evolving systems have the capacity to recruit additional variables that can be utilized to sustain the system and the ability to exclude variables that could destabilize the system.” Replication plays a key role in this process but requires the sequestering of “information-processing units”. Finally, there is two-way information flow between the slower-moving information units and the faster-changing data-collecting parts that interact with the environment. This, essentially, is learning how to stay alive.

 

What follows is an exposition of ten “basic phenomenological features of life” which the authors link to their theory of learning. I won’t go into these one-by-one, but rather pick out the concepts that I thought noteworthy. Let me preface this by commenting on the existence of a multiscale ‘situation’. It’s physico-chemical. The universe, and by extension Planet Earth, is made up of a mixture of multiple substances, which consists of molecules, which consists of atoms connected by vibrating bonds. Everything is in motion – it’s a dynamical system – but the timescales of motion are vastly different. Chemical bond vibrations are in the pico to femtosecond range. Molecules diffusing and colliding may be in the micro to nanosecond range. Nerves might pulse in a tenth of a second. I measure my time usage in minutes.

 

The inevitability of multiple distinct timescales is that different processes will ‘compete’ leading to frustrated states. But in addition to temporal frustration, there is also spatial frustration. This leads to a balance of sorts – an equilibrium, so to speak, but one that is semi-stable and may shift as the environment changes. Living systems that sequester their slow-changing informational systems that provide some organismal stability must continually receive and adapt to information being relayed from faster-changing ‘detector’ systems that interact directly with the environment. But neither of the two is privileged. It’s hard for us to think about this because we’re used to linear thinking of cause followed by effect. The lines of communication go both ways – a complex system where separation of the parts leads to death. You can’t separate the function of an organism from its genesis.

 

As to trial-and-error learning, the problem is it guarantees “neither finding the globally optimal solution nor retention of the optimal configuration when and if it is found. Rather stochastic optimization tends to rapidly find local optima and keeps the system in their vicinity”. Frustrated competing variables keep things that way. Not a necessarily bad thing since the environment will change. That’s why “biological evolution comprises numerous deleterious changes, comparatively rare beneficial changes and common neutral changes” that explain genetic drift, according to the authors. The diversity of local optima that arise from nonergodicity is why “evolution pushes organisms to explore and occupy all available niches and try all possible strategies”. We should expect a “diversity of solutions”.

 

Why do parasites show up? Diversity means that entities will arise that “scavenge information from the host” and “minimize their direct interface with the environment”. This may lead to symbiosis, but it might not. Competing imperatives are always in play. Why is there cell-programmed-death? There is an overall loss function to be minimized (the first principle!) and in a multicellular system, the tug-of-war between different scales could well result in reducing system failure by having individual cells (that have naturally accumulated problems – thanks, entropy) die off for the greater good.

 

To illustrate all this, the authors set up a (learning) neural network that has variables in different timescales. Some are ‘trainable’, others are not. There’s a logic to how they assign organismal versus environmental variables, and also how they divide the slower-changing variables into ones where changing them can be deleterious, neutral or adaptable. I won’t go into the math. Their conclusion: “slow variables determine the rules of the game, and changing these rules depending on the results of some particular games would be detrimental for the organism”, so it’s better to have “temporally stable rules” rather than an unconstrained optimization. But in the background, some of these rules can change. And as optimization continuously occurs dynamically, an environmental change may lead to a successful adaptation. Or it may lead to system failure.

 

Most important to me were the crucial setup of a system containing within it processes with distinct timescales, the inevitability of frustration, the role of renormalization, and determining what an appropriate loss function should be. The chemical systems I study (for which I build thermodynamic and kinetic maps) are likely too small. I’ve used the maximization of free energy reduction as the function to optimize, but perhaps I need to broaden or subdivide this into several mini-loss-functions. One of the papers that I didn’t discuss today goes into thermodynamics at a more general level and tries to connect it to the origin-of-life. They’re at a very abstract level, and the question is whether I can use their framework and fill in the details. It’s what keeps research interesting!